Ratios and Proportions


Proportions and Fractions

Proportions expressed as Fractions are Solved by Cross Multiplying.




Solving for X

(1) Set up the Fractions.


3
4

=
9
X




(2) Multiply the first Numerator with the second Denominator and place it to the Left of the Equal Sign.


3 X
=


(3) Multiply the first Denominator with the second Numerator and place it to the Right of the Equal Sign.


3 X
=
4 * 9

3X
=
36


(4) Solve for X by Dividing the Number Opposite the Equal Sign by the Number on the Same Side as the Equal Sign.


X
=
36
÷
3

X
=
12


(5) Prove the Answer by Replacing the Letter with the Number.


3
4

=
9
X




3
4

=
9
12




3 * 12
=
4 * 9


36
=
36


Both Products of the Cross Multiplication are Equal, therefore the Fraction Proportion is Equal and your Answer is Correct.




More Examples of Solving Fraction Proportions


7
5

=
14
X



7 X
=
5 * 14

7X
=
70

X
=
70
÷
7

X
=
10


7
5

=
14
X




7
5

=
14
10




7 * 10
=
5 * 14

70
=
70

* * * * * * *


1
20

=
X
100



1 * 100
=
20 X

100
=
20X

100
÷
20
=
X

5
=
X


1
20

=
X
100




1
20

=
5
100




1 * 100
=
20 * 5

100
=
100

* * * * * * *